Bayesian sample-size determination and adaptive design for clinical trials with Poisson outcomes.
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Hand, Austin L.
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Because of the high cost and time constraints for clinical trials, researchers often need to determine the smallest sample size that provides accurate inferences for a parameter of interest or need to adaptive design elements during the course of the trial based on information that is initially unknown. Although most experimenters have employed frequentist methods, the Bayesian paradigm offers a wide variety of methodologies and are becoming increasingly more popular in clinical trials because of their flexibility and their ease of interpretation. Recently, Bayesian approaches have been used to determine the sample size of a single Poisson rate parameter in a clinical trial setting. We extend these results to the comparison of two Poisson rates and develop methods for sample-size determination for hypothesis testing in a Bayesian context. Also, we propose a Bayesian predictive adaptive two-stage design for Poisson data that allows for sample-size adjustments by basing the second-stage sample size on the first-stage results. Lastly, we present a new Bayesian meta-analytic non-inferiority method for binomial data that allows researchers a more direct interpretation of their results. Our method uses MCMC methods to approximate the posterior distribution of the new treatment compared to a placebo rather than indirectly inferring a conclusion from the comparison of the new treatment to an active control.